SUO: Re: Laws, Facts, and Contexts
Rich,
Those are three very good questions, but before
answering your them, I'll start with a brief summary
of the paper on Laws, Facts, and Contexts in order
to emphasize the relevant points:
http://www.jfsowa.com/pubs/laws.htm
It presents a very general model-theoretic semantics
beginning with Dunn's work, which replaces Kripke's
possible worlds with Hintikka-style _model sets_,
which are sets of facts and takes Dunn's approach,
which extends Hintikka's set of propositions M
(called the facts of a world) with a subset L
of M (called the laws of that world).
Section 4 of that paper gives an informal example,
stated in bracketed English, of a person named Joe,
who says that he doesn't believe in astrology.
That is an example of how you can extend Dunn's
approach to beliefs. (And, by the way, you could
also consider that bracketed English as another
example of the use of controlled English for
representing a version of logic.)
Section 5 shows how Nested Graph Models can be
used to represent Dunn's semantics and their
extension to other modal logics, included
quantified modal logics and temporal logics.
Sections 6 uses the sample sentence "Tom believes
that Mary wants to marry a sailor" to show how
beliefs and desires can be represented in a
conceptual graphs. Then ir shows an NGM in terms
of which the model theory can evaluate the
denotation of that sentence. That is the basis
for supporting model theories of beliefs and
desires. Section 7 discusses various philosophical
implications of the theory.
RC> First, how can a BDI model be translated into
> an NGM? You gave some algorithms for translating
> other systems into NGMs, but not one for the BDI
> system you mentioned.
The example in Section 6 shows how beliefs and desires
can be handled in an NGM -- and the same NGM for both.
The representations of intentions that Levesque et al.
use for their BDI models could be handled in a similar
way. But I believe that a lot more has to be said
about intentions -- along the lines of Peirce's triads.
RC> Second, if an NGM model of a BDI system were
> implemented, would it be a good basis architecture
> for a question answering system that could capture
> WordNet, CoreLex, EVCA and other aspects of a
> large ontology for natural language processing
> instrumentation?
That is a paraphrase of a question I raised in Section 6
of the Laws paper:
JS> The nested contexts are governed by concepts such as
> Believe and Want, which represent two kinds of propositional
> attitudes. But natural languages have hundreds or thousands
> of verbs that express some kind of mental attitude about
> a proposition stated in a subordinate clause. How could the
> evaluation function take into account all the conditions
> implied by each of those verbs or the events they represent?
Section 7 of the paper presents further discussion of
Montague's approach and a brief discussion of how Peirce's
semeiotic provides a foundation for treating the kinds of
issues Montague was trying to address and relating them
to formal models based on NGMs. It concludes
JS> NGMs, by themselves, cannot solve all the problems of
> semantics, but they can incorporate ongoing research from
> logic, linguistics, and philosophy into a computable framework.
In other words, there is a lot of work to be done. The
people who are working on WordNet, CoreLex, etc., call their
work "lexical semantics" to distinguish it from "model-
theoreitc semantics". They don't even try to bring the two
kinds of semantics together. I believe that it is possible
to bring them together, and my paper gives some hints about
how to proceed. But it is a lot, a very big lot, of work.
RC> Third, what else would be needed for such an
> architecture to be fully capable of supporting
> question answering tasks in natural language?
Before we can handle full unrestricted NL, there are many
simpler problems that can be addressed. One way to handle
them is by extending versions of controlled NLs. Things
like CLCE are just a beginning, and there is more that
can be done. There is also a lot of things that can be
done in more informal ways as well. There is a lot more
to be said about both the formal and informal methods.
John